Ivory Black (PBk9) used to be made from charred ivory but is now just a marketing name for Bone Black; its colour varies a little but it can have a slightly brownish undercolour and will produce tints that are more neutral as a result.
Mars Black (PBk11) is an iron pigment, same family as the synthetic iron oxides; its colour varies a bit but it doesn't generally produce 'warm' greys.
As DaveMak mentions, which white is used has some bearing on what the tints of either will look like.
Since Dick Blick now have swatches for nearly all the paints on offer (as well as a second tab giving the pigment or pigments used) it's easy to see the variation in different versions by checking each of these from different makers. Compare the Gamblin version of
Mars Black with their version of
Ivory Black for example, should be easy to see how much more blue the tints of the former are.
Artie, there are a number of older threads where the common black and white pigments were asked about, here and in Oil Painting if you want to look up a bit more. If you work in layers, one thing mentioned in a few of them is that Mars Black is the leanest of the common black paints, the others being much more oily, so PBk11 is arguably a better choice for underpainting while any of the oilier ones would be better suited to upper layers.
Einion